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Lattices of choice functions and consensus problems

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Author Info
Bernard Monjardet ()
Vololonirina Raderanirina ()

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Abstract

In this paper we consider the three classes of choice functions satisfying the three significant axioms called heredity (H), concordance (C) and outcast (O). We show that the set of choice functions satisfying any one of these axioms is a lattice, and we study the properties of these lattices. The lattice of choice functions satisfying (H) is distributive, whereas the lattice of choice functions verifying (C) is atomistic and lower bounded, and so has many properties. On the contrary, the lattice of choice functions satisfying (O) is not even ranked. Then using results of the axiomatic and metric latticial theories of consensus as well as the properties of our three lattices of choice functions, we get results to aggregate profiles of such choice functions into one (or several) collective choice function(s). Copyright Springer-Verlag 2004

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File URL: http://hdl.handle.net/10.1007/s00355-003-0251-9
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Publisher Info
Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 23 (2004)
Issue (Month): 3 (December)
Pages: 349-382
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Handle: RePEc:spr:sochwe:v:23:y:2004:i:3:p:349-382

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July. [Downloadable!] (restricted)
  2. Monjardet, B., 1990. "Arrowian characterizations of latticial federation consensus functions," Mathematical Social Sciences, Elsevier, vol. 20(1), pages 51-71, August. [Downloadable!] (restricted)
  3. Johnson, Mark R. & Dean, Richard A., 2001. "Locally complete path independent choice functions and their lattices," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 53-87, July. [Downloadable!] (restricted)
  4. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May. [Downloadable!] (restricted)
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  1. Olivier Hudry & Bruno Leclerc & Bernard Monjardet & Jean-Pierre Barthélemy, 2004. "Médianes métriques et latticielles," Cahiers de la Maison des Sciences Economiques b04044, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
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